Chapter 7.1, Problem 7PB

Random variability in baseball A baseball player in the major leagues who plays regularly will have about 500 at-bats (that is, about 500 times he can be the hitter in a game) during a season. Suppose a player has a 0.300 probability of getting a hit in an at-bat. His batting average at the end of the season is the number of hits divided by the number of at-bats. When we consider the 500 at-bats as a random sample of all possible at-bats for this player, this batting average is a sample proportion, so it has a sampling distribution describing where it is likely to fall.

1. a. Describe the shape, mean, and standard deviation of the sampling distribution of the player’s batting average.
2. b. Explain why a batting average of 0.320 or of 0.280 would not be especially unusual for this player’s year-end batting average. (That is, you should not conclude that someone with a batting average of 0.320 is necessarily a better hitter than a player with a batting average of 0.280. Both players could have a probability of 0.300 of getting a hit.)